Let us start by envisaging what we would expect given the classical world in which we live. Imagine scaling this experiment up so you are firing tennis balls from a gun through slits in a sheet and on to a Velcro screen. Each ball will go through one slit or the other before sticking to the Velcro. You end up with two vertical lines of tennis balls on the Velcro screen that are determined by the positions of the gun and each of the slits.
In the quantum world, some of the atoms you fire appear to behave like scaled-down tennis balls. They will look as if they leave the end of the gun, go through one slit or the other in the sheet and will make a mark on the screen used to detect them. The mark, a slit and the gun will all lie on the same line. It turns out it is just luck that a few atoms behave like this, and most atoms will not behave like the tennis balls. Instead, other vertical lines of collisions between atoms and the screen will appear. A set of many parallel lines, separated by areas where no atoms are recorded, appears on the screen. Which slit did the atom go through when the screen records a mark that is not on a straight line with the gun or either of the slits? The answer is both: each atom goes through both of the slits at the same time. That is a truly mind-bending conclusion given our existence in the classical world where a tennis ball can go through only one slit or the other.
Each atom, and indeed any object, has waves associated with it. Each wave can be described with a mathematical expression called a wave function. The wave function for any object’s location describes all possible places where the object could be, along with the probability that the particle is in that part of the wave. For large objects with very small waves, the object will always appear in the same place. For small objects with large waves, the object can have a large number of places where it could be. For an atom, the wave can be viewed as describing all possible futures if it were to be forced to reveal its whereabouts as a particle. Objects can appear to be in two places when the wave function is bigger than the particle. When I mention a fuzz of electrons around an atomic nucleus, I am describing the wave function of the electrons.
In the film Men in Black 3, Michael Stuhlbarg plays a character called Griffin, an alien from the planet Archanan. These aliens are described as multidimensional beings who can see an infinite number of alternate timelines and possible futures. They are unable to predict which specific future will occur, but as particular events are realized some possible futures disappear while new ones emerge. Griffin uses this ability to steer the men in black to the only future that saves the world, and while doing so he admits that the ability to see so many options at once is a bit of a burden. I imagine it would be. Griffin’s power is a bit like seeing wave functions for the world around him. The wave functions he sees change as time passes, and so too do the possible futures, with some becoming more likely and others less so. A particle’s wave is a little bit like that. However, things in the quantum realm are even more bewildering.
There are various things you can measure about an atom, or an electron, or other particles, including their location and how fast they are moving. Each of these properties has a wave function associated with it, and the various wave functions are linked. What this means is that the more you find out about where, say, a particle is likely to be, the less you know about its speed. If you know where a particle is, you have no information about its velocity; and if you know how fast it is travelling, you have no idea where it is. The inability to know both of these things at once is called Heisenberg’s uncertainty principle, after the German physicist who first described it. The quantum world is based on uncertainties that scientists can describe with probabilities. The quantum behaviour of tiny particles and atoms is probabilistic, and ultimately it all boils down to their wave functions being larger than they are.
The wave function that describes where the atom could appear in the two-slit experiment creates what is known as an interference pattern, and it is this that creates the multiple vertical lines on the screen separated by areas where no atoms hit. One way to envisage an interference pattern is to think about the behaviour of water. Imagine a wave of water flowing towards two slits. It hits the slits and emerges on the other side. Semicircular expanding waves emanate from each slit. Each of these waves will move away from the slit before the waves collide with waves formed from the other slit. The collision generates an interference pattern of peaks and troughs in the watery waves. You can see something akin to this when the wakes from two boats meet. The water becomes choppy, with highs and lows. The same phenomenon happens with the wave function of the atom fired from the gun. The wave function of the atom is choppy, with highs describing where the particle is most likely to be, and lows where it is unlikely to show itself. The vertical stripes that form on the screen in the two-slit experiment are these highs, while the gaps between them are the lows. The two-slit experiment is a very clever way of using lots of atoms to reveal what an individual atom’s wave function looks like.
As an atom is fired from the gun it forms a wave which passes through the slits before the particle is coerced to emerge from the wave at a particular location on the detector screen. The slits must be close together for the experiment to work, and the width of each slit must be close to the wavelength – a property of the wave function – of the particle for an interference pattern to form. When these conditions are met, the experiment is repeatable, and the effect is always observed. All this raises the question, what makes the particle emerge from its wave and appear in one location on the screen?
When the atom in the two-slit experiment hits the screen, its wave function is said to collapse, and it reveals itself at a particular location. It would be a bit like you simultaneously leaving a building via both the front and back doors before magically appearing in one place in the street outside. The wave function describes an object’s wavelength. The bigger an object is, the smaller its wavelength becomes and the object appears in one location.
As an aside, large objects can be made to behave like small particles if the wavelengths of all their constituent atoms can be aligned in a particular way, but doing this is very difficult for anything larger than a single molecule. An approximate analogy for aligned wave functions is a line of metronomes ticking in perfect synchrony. In most cases, the atoms in an object are not synchronized like this but are more like a line of metronomes each doing its own independent thing. That is what happens in you. Your wavelength is about a billionth of a billionth of a billionth of a centimetre because the wave functions of your atoms are not in sync. Because you are much, much bigger than this, you behave as a solid object and we can ignore the wave function. If you were able to line up all the wave functions of each atom in your body, you would behave like a wave. You could behave like a quantum particle, leaving a building by multiple exits and appearing in the street. You are unable to line up your atoms’ wave functions, and this means the two-slit experiment won’t work for you, because you cannot fit through the extraordinarily narrow slits that would be required for the experiment to work. It would be like threading a camel through the eye of a very tiny needle. The two-slit experiment only works for objects that have wavelengths that are larger than they are, and these tend to be particles and atoms. For example, the wavelength of an electron is a couple of thousand times larger than the particle itself.
When an atom passes through a slit in the two-slit experiment and encounters the detector screen, it forms chemical bonds with the detector, becoming joined to the much larger object. The atom and screen have a wavelength, but because the wavelengths of the atoms in the screen are not aligned, the atom now appears in one place as part of the screen. If the atom were to be freed from the detector, it would regain its original quantum properties. As atoms join to form molecules, and molecules join to form large objects we can see, their wavelengths usually become unimportant for their behaviour, and they behave like objects we are familiar with in our everyday lives rather than like particles in the quantum world.